An introduction to K-theory for C*-algebras / M. Rørdam, F. Larsen, N. Laustsen.

Format:

Book

Author/Creator:

Rørdam, M. (Mikael), 1959- author.

Larsen, F. (Flemming), 1971- author.

Laustsen, N. (Niels), 1969- author.

Series:

London Mathematical Society student texts ; 49.

London Mathematical Society student texts ; 49

Language:

English

Subjects (All):

K-theory.

C*-algebras.

Physical Description:

1 online resource (xii, 242 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2000.

Language Note:

English

Summary:

Over the last 25 years K-theory has become an integrated part of the study of C*-algebras. This book gives an elementary introduction to this interesting and rapidly growing area of mathematics. Fundamental to K-theory is the association of a pair of Abelian groups, K0(A) and K1(A), to each C*-algebra A. These groups reflect the properties of A in many ways. This book covers the basic properties of the functors K0 and K1 and their interrelationship. Applications of the theory include Elliott's classification theorem for AF-algebras, and it is shown that each pair of countable Abelian groups arises as the K-groups of some C*-algebra. The theory is well illustrated with 120 exercises and examples, making the book ideal for beginning graduate students working in functional analysis, especially operator algebras, and for researchers from other areas of mathematics who want to learn about this subject.

Contents:

""Cover""; ""Tittle""; ""Copyright""; ""Contents""; ""Preface""; ""Chapter 1 C*-Algebra Theory""; ""1.1 C*-algebras and *-homomorphisms""; ""1.2 Spectral theory""; ""1.3 Matrix algebras""; ""1.4 Exercises""; ""Chapter 2 Projections and Unitary Elements""; ""2.4 Exercises""; ""2.1 Homotopy classes of unitary elements""; ""2.2 Equivalence of projections""; ""2.3 Semigroups of projections""; ""Chapter 3 The K0-Group of a Unital C*-Algebra ""

""3.1 Definition of the K0-group of a unital""""3.2 Functoriality of K0""; ""3.3 Examples""; ""3.4 Exercises""; ""Chapter 4 The Functor K0 ""; ""4.1 Definition and functoriality of K0 ""; ""4.2 The standard picture of the group K0(A) ""

""4.3 Half and split exactness and stability of K0 """"4.4 Exercises""; ""Chapter 5 The Ordered Abelian Group K0(A) ""; ""5.3 Exercises""

""5.1 The ordered K0-group of stably finite C*-algebras """"5.2* States on K0(A) and traces on A""; ""Chapter 6 Inductive Limit C*-Algebras""; ""6.5 Exercises""; ""6.1 Products and sums of C*-algebras""; ""6.2 Inductive limits""; ""6.3 Continuity of K0""; ""6.4* Stabilized C*-algebras""; ""Chapter 7 Classification of AF-Algebras""; ""7.1 Finite dimensional C*-algebras""; ""7.2 AF-algebras""

""7.3 Elliott's classification theorem""""7.4* UHF-algebras""; ""7.5 Exercises""; ""Chapter 8 The Functor K1""; ""8.4 Exercises""; ""8.1 Definition of the K1-group""; ""8.2 Functoriality of K1""; ""8.3* K1-groups and determinants""; ""Chapter 9 The Index Map""; ""9.1 Definition of the index map""; ""9.2 The index map and partial isometries""; ""9.3 An exact sequence of K-groups""; ""9.4* Fredholm operators and Fredholm index""; ""9.5 Exercises""; ""Chapter 10 The Higher K-Functors""; ""10.3 Exercises""; ""10.1 The isomorphism between K1(A) and K0(SA)""

""10.2 The long exact sequence in -RT-theory""

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 231-233) and indexes.

ISBN:

1-316-08781-6

0-511-62380-1

1-107-36800-6

1-107-36977-0

1-107-36309-8

0-511-82603-6

1-299-40918-0

1-107-36554-6

OCLC:

668201807